Generalizations of Mat\'ern's hard-core point processes

TL;DR

This paper generalizes Matérn's hard-core point processes by introducing a distance-dependent thinning rule, providing explicit formulas for their characteristics, and demonstrating applications in materials science.

Contribution

It extends Matérn's models to a broader class with explicit formulas and practical examples, enhancing their applicability in spatial statistics.

Findings

Explicit formulas for first- and second-order characteristics.

Application examples from materials science.

Generalized models with distance-dependent thinning.

Abstract

Mat\'ern's hard-core processes are valuable point process models in spatial statistics. In order to extend their field of application, Mat\'ern's original models are generalized here, both as point processes and particle processes. The thinning rule uses a distance-dependent probability function, which controls deletion of points close together. For this general setting, explicit formulas for first- and second-order characteristics can be given. Two examples from materials science illustrate the application of the models.